Rewrite as a simplified fraction. ${0.76\overline{4} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 764.4444...\\ 100x &= 76.4444...\end{align*}}$ Subtracting the two equations, we have: ${900x = 688}$ ${x = \dfrac{688}{900}} $ ${x = \dfrac{172}{225}} $